What is a multidimensional array?

A multidimensional array is a data structure where elements are organized across several dimensions (rows, columns, levels, etc.), that is, an array made up of other arrays.

In simpler terms, it's a way to store data as a table, a matrix, or a cube, rather than a single long line.

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#1. Example of a two-dimensional array

A two-dimensional array can be pictured as a table:

Here:

• A[0][0] = 1
• A[1][2] = 6
• A[2][1] = 8

This is an array of 3 rows and 3 columns.

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#2. Three-dimensional array

Can be pictured as a "data cube":

Example: B[2][1][0] is the element from the third layer, second row, first column.

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#3. Storage in memory

Even though visually this is a "table" or a "cube", in memory a multidimensional array is stored as a single contiguous sequence of elements.

There are two main placement methods:

• Row-major order: by rows (C, C++, Python)
• Column-major order: by columns (Fortran, MATLAB)

For example, for a 3×3 two-dimensional array, the elements [ [1,2,3], [4,5,6], [7,8,9] ] are stored one after another:

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#4. Formula for an element's address

For a two-dimensional array with n columns:

[ \text{address}(A[i][j]) = \text{base_address} + ((i \times n) + j) \times \text{size} ]

Where:

• i is the row number,
• j is the column number,
• size is the size of one element.

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#5. Uses

Multidimensional arrays are used in:

• mathematics (matrices, vectors),
• graphics (image pixels),
• machine learning (tensors),
• games and simulation (three-dimensional spaces).

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Summary:

A multidimensional array is an array whose elements are themselves arrays. It lets you store data as tables, matrices, or spatial grids and access elements using multiple indices.